Tonga took the lead early in the second half after Siegfried Fisiihoi crossed over Fiji's tryline.
Fiji are a win away over Tonga this weekend from lining up alongside Australia, Wales, Georgia and either Canada or Uruguay in Pool D of the 2019 Rugby World Cup.
Samoa will host Fiji next weekend and remains in competition with Tonga for the Oceania No. 2 qualifying position which would send it to the World Cup in a pool now comprising England, Argentina and France.
The third-placed team then face a playoff against a European side, with the loser of that game entering the repechage tournament.
The Oceania qualifying process is based on combined results of Pacific Nations Cup tournaments in 2016 and 2017.
They were seven points down in the second half but came back to beat Tonga 14-10
The Fijians won both of their games a year ago, beating Tonga 23-18 and Samoa 26-16 in Suva to notch up eight points.
Both sides were locked at 3-all at half-time.
In a tight contest at the Teufaiva Sport Stadium, Ben Volavola kicked three penalties while Leone Nakarawa got an important try to seal the win for Fiji.
Fiji is enjoying an outstanding season in which it has beaten Italy and Scotland before retaining the Pacific Nations Cup title.
Rooney Mara 'grossed out' by pie
She added, "It was such a unique way of showing grief; we've never seen anything like that before". More, she doesn't want to try it ever again.
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